Linda Darling-Hammond:
Remember that old game of telephone? One person whispered a message to another
who whispered it to another and so on until it came out an entirely different
message in the end.

When you talk to your students what do
they hear? What do they understand? And what can they remember and use
later?

The answers
to these questions have a lot to do with how all of us process information.
How can we teach so that our students can make sense of all the new ideas
they run into each day and use them effectively later?

I'm Linda Darling-Hammond and that's
our challenge for this session of The Learning Classroom.

When we introduce new material in the
classroom, each student makes sense of it in his or her own way.

One may remember a past experience and
then place the new material in a similar category. Another may hear only
a string of words until a "hands-on" experience is made available.
A third may misunderstand the information to make it fit better with what
he already knows. All of this is part of cognitive processing.

Roy
Pea, Ph.D., Stanford University: Cognitive processing is a
more technical term for phenomena that teachers and parents around the
world understand. Young kids think and reason and discuss and what
cognitive processing refers to is what is their mind doing as they do
those things. And, in the same way that a computer processes information
the mind processes information. And that's why the term cognitive
processing came about is, efforts to use computers to create models of
how humans reason and think.

Linda Darling-Hammond:
There are several things that teachers can do to help students process
and understand new information.

We can connect new ideas to the things
the students already know; we can present ideas in many different waysfor
example, visually, aurally, and "hands on" so that different
learners can get access to the information; we can use vivid representationspictures,
analogies, charts, graphs  that make the ideas come alive; we can
organize the information by identifying the big ideas and finding the
categories that create order among a lot of otherwise disconnected facts;
and we can make sure that students have a chance to really work with the
information.

Fe MacLean, a first grade teacher at
Paddock Elementary School helps her students organize what they're learning
so they develop a mental map for the new information.

Fe MacLean: In my classroom
every topic starts with a question. So, it's a mode of thinking.
It's a habit of thinking so, so that problems are really not problems.
They're questions to be answered.

(classroom scene)Fe: What are gills do you remember what gills
are? Yes Eric.
Eric: The things that they breathe through.Fe: Yep that's kind of like they don't have a nose. That's
kind of like their nose.

Fe MacLean: The initial
activity that I did was to give them lots, lots of pictures of animals
and my reasoning for doing that is because, well it's another way of learning.
It's, it's second hand knowledge. It's somebody else's first hand
knowledge that they have put either in photographs or on print.
And so, we will learn from what others already have experienced.
And by looking at these pictures the children decided how to group them.

(classroom scene)Girl: I do not like snakes.Boy: I like snakes.Girl 2: I love snakes.Fe: Well.Boy: Cool!

Fe MacLean: And then we look at each group,
for example, mammals. Why, why did you group these animals?
Why are they in one group? Well, they all have hair. Then we
talked about, oh, they walk, they all have legs the common things
about animals. Their babies look like their parents. And I will
ask questions to kind of draw them, draw the kinds of concepts that I want
them to draw.

(classroom scene)Fe: How do they move? The birds have wings, the fish
have tail. Yes Sarah? Which one of those has feet? Do they
all have feet?Student: Turtles and snakes.Fe: Okay some have feet.

Fe MacLean: The trip to
the museum is embedded in the unit of animals. We go to the
museum where they have Michigan animals and they are in these cases that
show habitat to some extent.

So before we went there we look at the,
some of their characteristics so when they go to the museum, they have
some background of what things they could look for.

After the children have connected their
ideas or their thinking from the pictures that we look at from the very
beginning of the lesson and some of the books they've looked at the museum
that we went to, what they saw there, and the videotape that they saw
they will construct a kind of a setting we call it setting because
we're relating it with setting for story. A habitat is a sort of
setting. And continue with their pop-up book which illustrates every
kind of animal that we have looked at.

Each page represents an, an eco ..is
a representative of a particular group of animals and then the child makes
a habitat or a setting for it. And so this is another one of the
aids to help me assess whether or not they're understanding the concepts
that we are learning.

(classroom scene)Fe: Is this the end of a sentence? Oh thank you. Good
thinking!

Linda Darling-Hammond:
Fe creates activities like the museum trip and the habitat project to
make what her students are learning come alive for them. As they engage
in these activities they process the information more deeply and they
draw more connections.

Fe MacLean: One of the
best ways for students to explain their thinking is through their writing.
That's where we inter in..interact with literacy in social studies
and science and, and really mostly anything. I use a lot of writing,
drawing, and then later on have the students explain to the, to the rest
of the class why they drew some things or why they wrote that what were
they thinking about when they wrote something.

(classroom scene)Fe: Can you read it to me?Boy: My grandma bought me a wooden reindeer at the craft
show.Fe: Did you go to the craft show at school? Oh, that's
neat. Who else came with you?Boy: My brother.

Fe MacLean: I use journals
as a free write for the students. They write anything they want.
The silly things, the complaints, anything at all. So it is a very good
tool for me to assess their thinking. In a cognitive sense, that clears
their mind about their thinking and writing. It's connecting together.
They rea they write it down, they read it. If it doesn't make
sense, they, they write it over. Or, they write, they think first
and then clarify their thinking so that they can put it on paper.
So, it is a tool in that sense.

(classroom scene)Girl: Today PBS came its weird but it is worth it and it is
cool. We are getting better at writing, it is fun.

Fe MacLean: With the
younger children, because they don't have any experiences with organizers,
we call them graphic organizers, I look at their thinking first and organize
them myself and they will see how they're organized. It's later
on when they're doing their own kinds of organizing or their own thinking
of their own writing ideas that they do borrow somehow from previous organizers
that been used in the classroom as a class.

(classroom scene)Fe: Ok, these were the some of the things you listed
out there that we needed. Ok, lets start reading it please.Class: Telephone, soap,
stove, car, refrigerator

Fe MacLean: For example
we recalled the needs of the family. And then I posed the question,
well what problems could arise with these needs of your families? So then
there's a problem and we brainstorm on, you know, for example, if a car
breaks down then we need a repair person or something like that.
And then I ask them to think together about problems that they might have
had at home.

(classroom scene)Fe: How do we know when the
shower is not working? Yes, Ashley.Ashley: The
water doesn't run,Fe: The water doesn't run, could we just say no water?Ashley: No water, yeah.Fe: Quicker to write .. Ok. How about lamp, how
do you know something's wrong with your lamp, Eric?Eric: It won't turn on.Student: The light bulb's burnt.

Fe MacLean: So in my writing
down on chart, I listed down the needs and I, I asked the question, I
put the, the problem right next to each one. And later on I drew
the lines to separate them and in, and in essence group them in different
ways.

Another way that they can explain their
thinking is to work in projects in tandem with another student or other
students.

If it is a community helper, because
maybe they have a common experience with that community helperlike
a mechanic or something like that. They both have common experience
of having their cars break down and their parents had to call a mechanic.
So, that is another way of explaining their thinking.

(classroom scene)Boy:I was a hundred miles from home when my car broke down.
I was!Girl: One day I was all the way in Ohio and our car broke down.Boy2: I was at my house.Girl: You're lucky.Boy: You're lucky! We had to call a tow truck to tow it to
P A T

Fe MacLean: In our lesson
today I will explain, not explain, but extend family needs to the whole
communitythat we really do need other helpers that may not be directly
helping your home or your family, but, but are helping in the general
community so that they do affect each individual family.

Fe MacLean: We come from
just the immediate need to bigger needs and there's where the bigger concepts
later on come from. And hopefully they continue to do that as they
go into higher and higher grades.

Linda Darling-Hammond:
Fe MacLean gives her students many ways to learn new material so that
everyone can find a connection that works for him or her. She
helps them develop categories to organize their thinking and she helps
them reason through the new concepts. By having
them talk, and write, and draw about their ideas, Fe encourages her students
to visualize as well as articulate their thinking.

Roy Pea: Visualizations
provide a new window into thinking beyond hearing students talk.
So a student who might be less verbally oriented may be quite willing
to draw a picture of how they're thinking about things and to even label
its parts in a way that can then become what we would call a conversational
prop for a learning conversationsomething that can be pointed at,
refined, talked about in a learning community in which all of the kids
in the classroom are creating visualizations. And part of what's
really interesting when a teacher does this, is that you find real differences
in the diagrams and the pictures that kids create.

Linda
Darling-Hammond: Sandie Gilliam is a tenth grade math teacher
from San Lorenzo Valley High School who introduces new concepts to her
students by building on their prior knowledge of history as well as mathematics.
She checks for misconceptions by getting them
to talk about what they think. She also uses
many ways to represent ideas so they connect for different learners. Finally,
she gets them actively engaged in making sense of the new concepts by
working through an authentic problem together.

Sandie Gilliam: I think
the kids need to have a hook of someplace they've been before. What
I try to do is connect it to something they've had before, an experience
they've had before or historical moment from another class or science
experiment, or say an Edgar Allen Poe story. And then I try to get
them in the mood of that, kind of get their mind in thinking about that
and then add little pieces that I can hook to pre-existing knowledge.

To the
observer with the discerning eye significant changes have come about in
the immigrant parties that assembled along the Missouri River towns of
1852 and 1853. By putting this lesson
in the context of the Oregon Trail they get
this visual image in their mind. And so we've got the historical
context and then I, I've added in variables. These kids have never been
exposed to algebraic variables before and in a way that they understand
the variable.

(classroom scene)Sandie:Twenty-five.Brett: Men in a wagon train.Sandie: Twenty-five men
in the wagon train. So that makes sense to everybody right?

Sandie Gilliam: And by
putting the variables in the context of the Overland Trail, they have
really understood and made their own equations strictly with variables
and it just really builds up their, their knowledge base. And so
now we've started graphing. So again we're connecting to the Overland
Trail story that I read and we're connecting to the variable that they
used. So it's reinforcing that concept of variable and now we're
translating it to a graph to see pictorially what would that look like.

(classroom scene)Sandie: We're doing the graphing on the Overland Trail that
we're starting to do. You're gonna have to make sense of what the
graph is showing you. And you're gonna have to think about these things,
what time of day it is, what's the weather like, how many people are on
the trip, all of that is going to have to come into your mind and into
play and looking at graphing.

Kris Neustadter: Our math
program here uses, just by virtue of what it is, we use a number of visual
aids to start with. So a kid who has an auditory problem, processing
problem, where they're not necessarily hearing what Sandie's saying to
introduce a unit or what I'm saying, what we have for them as we go into
a unit are diagrams. For instance just one of the things that I think
has been really helpfulthe kids had to create a list of what they
wanted to take on the Overland Journey trail. And, and we started
out with a sheet that just had all these different supply items.

So even if a kid never heard anything
we explained, we had that sheet that was simple and to the point where
they could see what needed to go and they had to actually do something
with them besides manipulating numbers. Almost everything we do
in math here will start out with words and on the board in the big group,
and then we bring it down to more individual ways of teaching everybody
and with many visual aids.

(classroom scene)Sandie: Does that make sense
now? Could you put the next point there for me? So I know you know it.

Sandie Gilliam: Rather
than just start at the beginning of what graphing is, I wanted to see
what kind of background they all brought to the graphing. And so
I noticed what was happening and that's very interesting for me as a teacher
to see where the holes are, what the memories are, what the kids are perceiving
with graphing.

Roy Pea: These beliefs
that they have are important to understand for us to go building on in
instruction. So, prior conceptions, some call them misconceptions, we
prefer to call them prior conceptions. Are, one very significant
influence that work in the learning sciences is help reveal over the last
number of years and that I think teaching can really pay attention to.

(classroom scene)Sandie: So let's look at
what a graph of this would look like. Okay, who thinks they could come,
they know enough about graphing from back in junior high that they could
come and actually make a graph of this? Ok, Brett? Would you stop
and explain, so I can see what you are doing? What do those mean?Brett: Well,
there's no one to it. There's two families with four men and there's five
families with ten men.Sandie: Okay, does a graph normally, ah does
a graph normally have those boxes on it?

Sandie Gilliam: When Brett
came to the board to do his graph for that equation Y is equal to 2X,
I noticed he was putting those boxes and was trying to figure out if that
was some method. I mean, he wasn't plotting points, he was making
boxes.

And I was afraid of the rest of the class
thinking that boxes was a part of what we needed to do, and then had to,
to switch in my mind and get the kids to realize that I was really just
looking at the points that represented the data
from the in and out table.

(classroom scene)Sandie: What should I see when I'm looking at a
graph? Instead of boxes? What was that?Jamie: Dots.Sandie: Dots! Ok, and where would the dots be located, Jamie,
the points?Jamie: The corner of each of those boxes.Sandie: The corner of each of those boxes. Thank you Brett.

Sandie Gilliam: I like
to ask kids questions. I don't like to ask them a whole lot of one-answer
questions, like how many sides are in a triangle? Three. I,
I like to ask them deep questions, you know. What do you notice
about those points on the line? Why do you think that happens?
I want to hear how they process.

(classroom scene)Sandie: Ok, so we don't have a line, do we have
a ray?Class: Yes. Maybe.Sandie: I want you to think about it, do we have a ray in this
situation?Boy: Well, right now.Sandie: We connected those points with the line, that's what
Brett did. And you extended the line up to this point and they're all
on the line. All of these X's are on the line.Girl: There is no point at the zero. It's like there's a line,
but there's no point at the end.Sandie: Should there be a point at the end?Girl: No, cause there's no zero.Sandie: Ok, she says there's no zero over here on the charts.
There can be? Why can there be?Boy: Because it's there needs to be a starting point.Other students: "Starting point is zero." "But
you can start at zero." "You can have zero men and zero
families."Sandie: I can have zero men and zero families, does that make
sense?Class: Yeah.

Sandie Gilliam: I try to get my kids up
to the board and, and ask those questions. They have to go up and they have
to explain what they're doing.

(classroom scene)Girl: Ok, you start out on the trip with like a
full stock of coffee.Sandie: Well, what do you suppose a full stock of coffee might
be?Girl: Like, 500 I don't know.Sandie: Fine, 500 pounds of coffee. Why don't you put 500 up
there.

Sandie Gilliam: And then
they have to answer questions from their peers, and then they have to
answer the questions from me that are related to what they did.
But they have to thoroughly understand what they're doing.

What it does is the other students in
the classroom learn too, because they want to protect or help the person
at the board, they have to pay attention so much more.

(classroom scene)Girl: Is that wrong?Other student: No, keep going!Sandie: Who has the, what you can do is turn to them and ask
for suggestions.Girl: Suggestions? Brett?Brett: First day, second day, third day.Sandie: The person at the board's gotta think the students
that are sitting back have to think, because they know those questions
aren't going away and I'm not answering the questions.Sandie: Now can you explain the graph?Girl: Day one, they start out with 500 pounds of coffee. Day
two, they drink some of it and they have 375.

Sandie Giliam: And especially
with a class where you have low self-esteem or you have special needs
students. There has to be a lot of different ways of interpreting
the information, whether it's visual or kinesthetic. They have to find
a way that deep thinking happens.

(classroom scene)Sandie: I love these questions because again we have to, well,
we don't know how many people are on the trip, but we have to figure out
what you know and what you don't know.

Sandie Gilliam: Many times
people just plot graphs and kids don't understand the concept or the meaning,
what's happening in the graph. So, if we take away the data and
we just use a scaling, like over time, can the kids interpret graphs and
can they understand what's happening when graphs have dips or when graphs
have straight lines? Can they, can they look at that and think about it
rather than just plotting individual points on graphs and it just becomes
an exercise in can you plot points? I want it to be looking at data and
understanding data.

(classroom scene)Sandie: Kyle said they didn't take any water here
or they didn't drink any water here. Why?Boy: Like when they, started out with lots of water and then
they drank a lot.Sandie: And how do you know that they drank a lot?Boy: Because it went down.Sandie: Say it again, you used the word drop. That was the
word I was looking.Boy: It dropped down.Sandie: Which means they?Boy: Drank a lot of water.Sandie: A lot of water? Did they drink a little water?Boy: No, then they, when it flatlines they were very conservative
until they, till they got to the stoppage point to restock. Then it went
up.Sandie: And why would?Boy: Because they got all their water back and then they went
down again, they flatlined, and then it's gonna probably be stocking up
again.Sandie: Ok, does that make sense?Student: Yeah.Sandie: Ok, um can someone tell me at which spot did they drink
faster? At this spot or at this spot?

Kris Neustadter: They need
to know that they're learners and they need to know that they can translate
what they learn in math class to history class, especially with the Overland
Trail or that they can translate what they're doing here, a thought process,
to their English class when they're brainstorming ideas for their English
paper.

Sandie Gilliam: We wanted
to create a class that was, that, that met the needs of all kinds of learners,
that all kinds of intelligences. So we have interpersonal and, and
intrapersonal and we have kinesthetic learners and we have musical learners
and we have visual learners and all of Gardner's different intelligences
and we try to make sure that however kids learn and process that the class
holds something for them.

Roy Pea: Part of what this
teacher does that's extremely useful is setting the problem solving context
in a motivational one of human narrative and drama. And that helps
attract students attention, probably relates to situations they could
imagine themselves in, as opposed to being simple, dry, decontextualized
formula. She then gives them the opportunity for reasoning quantitatively
about their use of supplies during their trip, water in particular.
And so they then have the opportunity to talk about what the shape of
a graph would look like for water availability at different times in the
trip.

Linda Darling-Hammond: Fe
MacLean and Sandie Gilliam take time to attend to their students' thoughts
as well as their actions.

They help students organize their thinking,
and they encourage them to present their learning so the class can see
many ways to think about a new concept.

Roy Pea: People that have
studied even elementary school children's understanding of memory, of
language, of reasoning, they're quite reflective about these things.
They recognize that when they're tired or distracted, they don't do as
well, they don't remember as much. So they're attentive to cognitive
processing. What teachers can help bring to the equation from the
learning sciences is much more attention to teasing out what their learners
are thinking and believing by having them represent that knowledge in
conversations, in pictures and in other modalities.

Linda Darling-Hammond:
The many different ways human beings think and learn is part of what makes
us who we are.

When we adapt our teaching to help all
kinds of thinkers acquire, and understand, and apply new ideas we help
them create meaning both for the classroom and for life.